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Upper Bounds for the Essential Dimension of $E_7$

Published:2013-03-20

• Mark L. MacDonald,
Department of Mathematics and Statistics, Fylde College, Lancaster University, Bailrigg, Lancaster LA1 4YF, United Kingdom
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Abstract

This paper gives a new upper bound for the essential dimension and the essential 2-dimension of the split simply connected group of type $E_7$ over a field of characteristic not 2 or 3. In particular, $\operatorname{ed}(E_7) \leq 29$, and $\operatorname{ed}(E_7;2) \leq 27$.
 Keywords: $E_7$, essential dimension, stabilizer in general position
 MSC Classifications: 20G15 - Linear algebraic groups over arbitrary fields 20G41 - Exceptional groups